Photonic band gaps, strong light-matter interaction, slow light, and negative refractive index arise in photonic crystal structures due to Bragg scattering of electromagnetic waves from a repeated unit cell. See E. Yablonovitch et al., Phys. Rev. Lett. 67, 2295 (1991); T. Yoshie et al., Nature 432, 200 (2004); T. Baba, Nature Photon. 2, 465 (2008); A. Berrier et al., Phys. Rev. Lett. 93, 073902 (2004); E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987); and S. John, Phys. Rev. Lett. 58, 2486 (1987). However, the electromagnetic properties of photonic crystals engineered from bulk semiconductors, metals, and dielectrics generally are weakly tunable, if at all. Material systems such two-dimensional electron gases (2DEGs) embedded in semiconductors and graphene offer a substantially more flexible electromagnetic medium. See S. J. Allen et al., Phys. Rev. Lett. 38, 980 (1977); M. I. Dyakonov and M. S. Shur, IEEE Trans. on Electron Devices 43, 380 (1996); L. Ju et al., Nature Nano. 6, 630 (2011); H. Yan et al., Nature Nano. 7, 330 (2012); and A. N. Grigorenko et al., Nature Photon. 6, 749 (2012). These plasmonic materials can both be lithographically patterned and electronically tuned, giving rise to a variety of subwavelength plasmonic devices that may be broadly controlled via an applied DC electric field. When a periodic structure is engineered from these systems, a plasmonic band structure can be realized. See U. Mackens et al., Phys. Rev. Lett. 53, 1485 (1984); V. M. Muravev et al., Phys. Rev. Lett. 101, 216801 (2008); G. C. Dyer et al., Phys. Rev. Lett. 109, 126803 (2012); and W. F. Andress et al., Nano Lett. 12, 2272 (2012).
However, a need remains for a tunable plasmonic band structure, i.e., a tunable plasmonic crystal. The present invention provides widely tunable plasmonic band gap structures using a two-dimensional electron or hole gas in semiconductors or graphene.